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;                                               Appendix II.                             861

*                if E shew energy as delivered from a rifle bullet (W#2/2 g) while

A,               penetrating a target to depth 4 the pressure exerted at any point

will be shewn by the/ ordinates. Therefore force is rate of energy
change regarding distance. If, however, the curve/ be drawn to
a time base as at D, summation will give momentum, or (W#/£•),
for momentum = impulse or ft. Then, for a second definition,
force is rate of change of momentum regarding time. These
principles may be carried much further: thus, kinetic energy is
the sum of \v regarding momentum and so on.

Speaking next of curve averages, it will be easily seen that
average velocity, for example, will depend on the base units, and
that a time-base average can only equal a distance-base average in
the case of uniform velocity, for then distances are proportional
to times, and the curves are exactly alike (see E). Uniformly
accelerated velocity is shewn at F for both time and distance
bases, and the average v is evidently less in the former than
the latter. In like manner there are time- and distance-base
averages of force, as at D and c respectively, a steam-engine-
indicator mean pressure being a distance average. {See p. 1099.)

P. 478. Energy Curves.

Example 63.—A steam piston of a horizontal engine is 30 ins.
diameter, and the net propelling forces due to the steam in Ibs. per
sq. in., at 6 in. intervals of stroke, are as follows : 100, 98, 97, 96, 95,
79, 67, 57, 49, 43, 3*, 34i, 3*, 28, 25, 23, 21, £c. The resistances of
load and friction are 19 tons, assumed constant, and the weight of the
moving parts is taken at 6 tons. Find the correct length of stroke and
draw the velocity curve. (Hons. Applied Mechs. Exam., 1897, slightly

Draw any horizontal base A B, Fig. 824, and set out the 6 in.
spaces as shewn. Erect verticals, plot total net steam pressure in
ton's =p (piston area--2240) = "315^, and draw hyperbolic curve
C Q r>. As the piston advances from left to right, the area under this
curve shews, total energy up to a given position. Summate then
curve C Q D, and obtain curve A M F of total energy (see p. 860). The
scale for B F is obtained from previous explanations. Draw G H so that
AG = P the total load resistance, = 19 tons. Now, energy absorbed
by load is P x D, where D is the stroke swept out up to any point,
and the summation of G H, with same pole P, gives A L j, the curve
of load energy measurable to same scale as B F. But generally—